Gravity, Scale Invariance and the Hierarchy Problem

TL;DR

This paper explores how non-perturbative effects, involving instantons and scale invariance, could explain the hierarchy between the electroweak and Planck scales within a scale-invariant framework combining the Standard Model and gravity.

Contribution

It proposes a novel non-perturbative mechanism involving instantons that generates the hierarchy, integrating scale invariance with gravity and the Standard Model.

Findings

Instanton configurations contribute to Higgs vacuum expectation value.

Scale invariance combined with gravity stabilizes the electroweak scale.

A non-perturbative effect can generate the hierarchy without new particles.

Abstract

Combining the quantum scale invariance with the absence of new degrees of freedom above the electroweak scale leads to stability of the latter against perturbative quantum corrections. Nevertheless, the hierarchy between the weak and the Planck scales remains unexplained. We argue that this hierarchy can be generated by a non-perturbative effect relating the low energy and the Planck-scale physics. The effect is manifested in the existence of an instanton configuration contributing to the vacuum expectation value of the Higgs field. We analyze such configurations in several toy models and in a phenomenologically viable theory encompassing the Standard Model and General Relativity in a scale-invariant way. Dynamical gravity and a non-minimal coupling of it to the Higgs field play a crucial role in the mechanism.